Abstract
A theory admits generalized conformal structure if the only scale in the quantum theory is set by a dimensionful coupling. SYK is an example of a theory with generalized conformal structure and in this paper we investigate the consequences of this structure for correlation functions and for the holographic realization of SYK. The Ward identities associated with the generalized conformal structure of SYK are implemented holographically in gravity/multiple scalar theories, which always have a parent AdS3 origin. For questions involving only the graviton/running scalar sector, one can always describe the bulk running in terms of a single scalar but multiple running scalars are in general needed once one includes the bulk fields corresponding to all SYK operators. We then explore chaos in holographic theories with generalized conformal structure. The four point function explored by Maldacena, Shenker and Stanford exhibits exactly the same chaotic behaviour in any such theory as in holographic realizations of conformal theories i.e. the dimensionful coupling scale does not affect the chaotic exponential growth.
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References
S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
A. Kitaev, A simple model of quantum holography (part 1), talks at KITP, University of California, Santa Barbara CA U.S.A., 7 April 2015.
A. Kitaev, A simple model of quantum holography (part 2), talks at KITP, University of California, Santa Barbara CA U.S.A., 27 May 2015.
D.J. Gross and V. Rosenhaus, A generalization of Sachdev-Ye-Kitaev, JHEP 02 (2017) 093 [arXiv:1610.01569] [INSPIRE].
E. Witten, An SYK-like model without disorder, arXiv:1610.09758 [INSPIRE].
W. Fu, D. Gaiotto, J. Maldacena and S. Sachdev, Supersymmetric Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 026009 [Addendum ibid. D 95 (2017) 069904] [arXiv:1610.08917] [INSPIRE].
I.R. Klebanov and G. Tarnopolsky, Uncolored random tensors, melon diagrams and the Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 046004 [arXiv:1611.08915] [INSPIRE].
T. Nishinaka and S. Terashima, A note on Sachdev-Ye-Kitaev like model without random coupling, Nucl. Phys. B 926 (2018) 321 [arXiv:1611.10290] [INSPIRE].
C. Peng, M. Spradlin and A. Volovich, A supersymmetric SYK-like tensor model, JHEP 05 (2017) 062 [arXiv:1612.03851] [INSPIRE].
C. Krishnan, S. Sanyal and P.N. Bala Subramanian, Quantum chaos and holographic tensor models, JHEP 03 (2017) 056 [arXiv:1612.06330] [INSPIRE].
G. Turiaci and H. Verlinde, Towards a 2d QFT analog of the SYK model, JHEP 10 (2017) 167 [arXiv:1701.00528] [INSPIRE].
T. Li, J. Liu, Y. Xin and Y. Zhou, Supersymmetric SYK model and random matrix theory, JHEP 06 (2017) 111 [arXiv:1702.01738] [INSPIRE].
M. Berkooz, P. Narayan, M. Rozali and J. Simón, Comments on the random Thirring model, JHEP 09 (2017) 057 [arXiv:1702.05105] [INSPIRE].
C. Krishnan, K.V.P. Kumar and S. Sanyal, Random matrices and holographic tensor models, JHEP 06 (2017) 036 [arXiv:1703.08155] [INSPIRE].
C. Peng, Vector models and generalized SYK models, JHEP 05 (2017) 129 [arXiv:1704.04223] [INSPIRE].
T. Kanazawa and T. Wettig, Complete random matrix classification of SYK models with N = 0, 1 and 2 supersymmetry, JHEP 09 (2017) 050 [arXiv:1706.03044] [INSPIRE].
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional nearly anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
J. Polchinski and V. Rosenhaus, The spectrum in the Sachdev-Ye-Kitaev model, JHEP 04 (2016) 001 [arXiv:1601.06768] [INSPIRE].
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
A. Jevicki and T. Yoneya, Space-time uncertainty principle and conformal symmetry in D particle dynamics, Nucl. Phys. B 535 (1998) 335 [hep-th/9805069] [INSPIRE].
A. Jevicki, Y. Kazama and T. Yoneya, Quantum metamorphosis of conformal transformation in D3-brane Yang-Mills theory, Phys. Rev. Lett. 81 (1998) 5072 [hep-th/9808039] [INSPIRE].
A. Jevicki, Y. Kazama and T. Yoneya, Generalized conformal symmetry in D-brane matrix models, Phys. Rev. D 59 (1999) 066001 [hep-th/9810146] [INSPIRE].
N. Itzhaki, J.M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large-N limit of theories with sixteen supercharges, Phys. Rev. D 58 (1998) 046004 [hep-th/9802042] [INSPIRE].
I. Kanitscheider, K. Skenderis and M. Taylor, Precision holography for non-conformal branes, JHEP 09 (2008) 094 [arXiv:0807.3324] [INSPIRE].
I. Kanitscheider and K. Skenderis, Universal hydrodynamics of non-conformal branes, JHEP 04 (2009) 062 [arXiv:0901.1487] [INSPIRE].
A. Jevicki, K. Suzuki and J. Yoon, Bi-local holography in the SYK model, JHEP 07 (2016) 007 [arXiv:1603.06246] [INSPIRE].
M. Cvetič and I. Papadimitriou, AdS 2 holographic dictionary, JHEP 12 (2016) 008 [Erratum ibid. 01 (2017) 120] [arXiv:1608.07018] [INSPIRE].
S.R. Das, A. Jevicki and K. Suzuki, Three dimensional view of the SYK/AdS duality, JHEP 09 (2017) 017 [arXiv:1704.07208] [INSPIRE].
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].
D.A. Roberts, D. Stanford and L. Susskind, Localized shocks, JHEP 03 (2015) 051 [arXiv:1409.8180] [INSPIRE].
D.A. Roberts and D. Stanford, Two-dimensional conformal field theory and the butterfly effect, Phys. Rev. Lett. 115 (2015) 131603 [arXiv:1412.5123] [INSPIRE].
A. Jevicki and K. Suzuki, Bi-local holography in the SYK model: perturbations, JHEP 11 (2016) 046 [arXiv:1608.07567] [INSPIRE].
A.M. Garcıa-García and J.J.M. Verbaarschot, Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 126010 [arXiv:1610.03816] [INSPIRE].
A.M. García-García and J.J.M. Verbaarschot, Analytical spectral density of the Sachdev-Ye-Kitaev model at finite N , Phys. Rev. D 96 (2017) 066012 [arXiv:1701.06593] [INSPIRE].
D.J. Gross and V. Rosenhaus, The bulk dual of SYK: cubic couplings, JHEP 05 (2017) 092 [arXiv:1702.08016] [INSPIRE].
S. Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105 (2010) 151602 [arXiv:1006.3794] [INSPIRE].
S. Sachdev, Bekenstein-Hawking entropy and strange metals, Phys. Rev. X 5 (2015) 041025 [arXiv:1506.05111] [INSPIRE].
H.J. Boonstra, K. Skenderis and P.K. Townsend, The domain wall/QFT correspondence, JHEP 01 (1999) 003 [hep-th/9807137] [INSPIRE].
M.J. Duff, G.W. Gibbons and P.K. Townsend, Macroscopic superstrings as interpolating solitons, Phys. Lett. B 332 (1994) 321 [hep-th/9405124] [INSPIRE].
B. Gouteraux, J. Smolic, M. Smolic, K. Skenderis and M. Taylor, Holography for Einstein-Maxwell-dilaton theories from generalized dimensional reduction, JHEP 01 (2012) 089 [arXiv:1110.2320] [INSPIRE].
D.J. Gross and A. Neveu, Dynamical symmetry breaking in asymptotically free field theories, Phys. Rev. D 10 (1974) 3235 [INSPIRE].
K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [INSPIRE].
K. Jensen, Chaos in AdS 2 holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].
M. Blake and A. Donos, Diffusion and chaos from near AdS 2 horizons, JHEP 02 (2017) 013 [arXiv:1611.09380] [INSPIRE].
J.S. Cotler et al., Black holes and random matrices, JHEP 05 (2017) 118 [arXiv:1611.04650] [INSPIRE].
R.A. Davison, W. Fu, A. Georges, Y. Gu, K. Jensen and S. Sachdev, Thermoelectric transport in disordered metals without quasiparticles: the Sachdev-Ye-Kitaev models and holography, Phys. Rev. B 95 (2017) 155131 [arXiv:1612.00849] [INSPIRE].
M. Mezei, S.S. Pufu and Y. Wang, A 2d/1d holographic duality, arXiv:1703.08749 [INSPIRE].
K. Skenderis and B.C. van Rees, Real-time gauge/gravity duality, Phys. Rev. Lett. 101 (2008) 081601 [arXiv:0805.0150] [INSPIRE].
K. Skenderis and B.C. van Rees, Real-time gauge/gravity duality: prescription, renormalization and examples, JHEP 05 (2009) 085 [arXiv:0812.2909] [INSPIRE].
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Taylor, M. Generalized conformal structure, dilaton gravity and SYK. J. High Energ. Phys. 2018, 10 (2018). https://doi.org/10.1007/JHEP01(2018)010
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DOI: https://doi.org/10.1007/JHEP01(2018)010